Finite Group Databasebeta

← #26028327

Subgroups — #26028327

Order 11392.

456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15668007C212yesmaximal, complemented
2#19151532C212yesmaximal, complemented
3#19151522C212yesmaximal, complemented
4#19151520C212yesmaximal, complemented
5#19151520C212yesmaximal, complemented
6#19151516C212yesmaximal
7#19151515C211yesmaximal, characteristic
8#19151467C211yesmaximal, characteristic, complemented
9#398×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11#15668007—28no—
12C2×C4⋊Dic89C2212yes—
13C2×C4⋊Dic89C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×#13083553C2212yes—
17C2×#13083553C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×C4×Dic89C2211yescharacteristic
25#15667919C2211yescharacteristic
26#15667919C2212yes—
27C2×C4⋊C4×C89C2212yes—
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2211yescharacteristic
30#95×C89C2212yes—
31#95×C89C2211yescharacteristic
32C23×D89C2312yes—
33C2×D356—41no—
34C2×D356—42no—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C4⋊Dic89—24no—
39C4⋊Dic89—41no—
40#13083553—24no—
41#13083553—42no—
42#13083553—42no—
43#13083553—42no—
44#13083551—24no—
45#13083551—24no—
46#13083551—24no—
47#13083551—42no—
48#13083551—42no—
49#13083551—42no—
50C4×Dic89D414yescomplemented
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2312yes—
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C22×C4×C89C2311yescharacteristic
56C4⋊C4×C89—24no—
57C4⋊C4×C89—41no—
58C4⋊C4×C89—41no—
59C23×C89C2411yescharacteristic
60C22×D89—22no—
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C22×D89—22no—
65C22×D89—22no—
66C22×D89—22no—
67C2×C4×C89—21no—
68C2×C4×C89—21no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—21no—
72C2×C4×C89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89C2×D412yes—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89C2×D414yes—
89D356—44no—
90C22×C89C22×D411yescharacteristic
91C22×C89H(5,𝔽2)11yescharacteristic
92C22×C89H(5,𝔽2)12yes—
93C22×C892−1+411yescharacteristic
94C22×C892−1+412yes—
95C2×D89—42no—
96C2×D89—42no—
97C2×D89—42no—
98C2×D89—42no—
99C2×D89—42no—
100C2×D89—42no—
101C2×D89—42no—
102C4×C89—22no—
103C4×C89—42no—
104C4×C89—42no—
105C4×C89—41no—
106C4×C89—41no—
107Dic89—24no—
108Dic89—42no—
109Dic89—42no—
110C2×C89#53711yescharacteristic
111C2×C89#53712yes—
112C2×C89#56011yescharacteristic
113C2×C89#56311yescharacteristic
114C2×C89#56312yes—
115D89—82no—
116#2823—891nomaximal, Sylow
117C89#282311yescharacteristic, complemented, Sylow
118C2×#126—892no—
119#398—892no—
120#398D8911yescharacteristic, complemented
121#396—892no—
122#396—892no—
123#396—892no—
124#394—891no—
125#394—892no—
126#384—891no—
127C22×D4—891no—
128#126—1788no—
129C2×C4⋊C4—892no—
130C2×C4⋊C4—892no—
131C2×C4⋊C4—891no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—892no—
134C2×C4⋊C4—892no—
135C2×C4⋊C4C2×D8912yes—
136C2×C4⋊C4C2×D8911yescharacteristic
137C2×C4⋊C4C2×D8911yescharacteristic
138C2×C22⋊C4—892no—
139C2×C22⋊C4—892no—
140C2×C22⋊C4—892no—
141C2×C22⋊C4—892no—
142C2×C22⋊C4—892no—
143C2×C22⋊C4—892no—
144C2×C42—891no—
145#95—891no—
146#95—892no—
147#95C2×D8912yes—
148#95C2×D8911yescharacteristic
149C24—892no—
150C2×D4—3561no—
151C2×D4—3562no—
152C22×C4—892no—
153C22×C4—892no—
154C22×C4—892no—
155C22×C4C22×D8911yescharacteristic
156C22×C4C22×D8912yes—
157C22×C4C22×D8912yes—
158C22×C4C22×D8911yescharacteristic
159C22×C4C22×D8911yescharacteristic
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—3562no—
164C4⋊C4—3562no—
165C4⋊C4—3562no—
166C4⋊C4—3561no—
167C4⋊C4—1784no—
168C4⋊C4—1784no—
169C22⋊C4—3562no—
170C22⋊C4—3562no—
171C22⋊C4—3562no—
172C22⋊C4—1784no—
173C22⋊C4—1784no—
174C22⋊C4—1784no—
175C42—894no—
176C23—1782no—
177C23—1782no—
178C23—1782no—
179C23—1782no—
180C23—1782no—
181C23—1782no—
182C23—1782no—
183C23C23×D8911yescharacteristic
184D4—3564no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—894no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4D4×D8912yes—
207C22—3562no—
208C22—3562no—
209C22—3562no—
210C22—3562no—
211C22—3562no—
212C22—3562no—
213C22—3562no—
214C22C2×D4×D8911yescharacteristic
215C22#1566805711yescharacteristic
216C22#1566805812yes—
217C22#1566805911yescharacteristic
218C22#1566806012yes—
219C4—22no—
220C4—42no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—3562no—
225C4—3562no—
226C4—1784no—
227C2—7122no—
228C2#1915217511yescharacteristic
229C2#1915217812yes—
230C2#1915233811yescharacteristic
231C2#1915234711yescharacteristic
232C2#1915235212yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC22×D356C22
hypercenter#398D89
hypocenterC89#2823
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#15668007C2semidirect
2. #19151532C2semidirect
3. #19151522C2semidirect
4. #19151520C2semidirect
5. #19151520C2semidirect
8. #19151467C2semidirect
9. #398×C89C2semidirect
50. C4×Dic89D4semidirect
117. C89#2823semidirect
120. #398D89semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156680072
#191515322
#191515222
#191515202
#191515162
#191515152
#191514672
#398×C892
#282389